1. Field of the Invention
The invention relates, in general, to reciprocating machines for converting thermal energy into mechanical force or, conversely, using mechanical work to transfer thermal energy from one region to another. In particular, the invention relates to mechanisms designed to produce position-dependent conservative forces to counter the conservative forces that arise from the change in volume of the machine's working medium.
2. Description of the Prior Art
Conservative forces are defined as those forces that are a direct result of a potential energy field and, therefore, are a function only of position. As a consequence, it is sufficient and necessary that they derive from the gradient of a potential energy function. The work a conservative force does on an object in moving it from point A to B is path independent—i.e., it depends only on the end points of the motion. For example, the force of gravity and the spring force are conservative forces owing to their dependence only on a parameter of position. By contrast, a spinning flywheel represents kinetic energy that is a function not of its orientation, but of a change in its orientation as a function of time. Therefore, a force resulting from a spinning flywheel cannot be the gradient of a potential energy function and, subsequently, cannot be a conservative force. Other examples include dissipative forces such as friction and air-resistance which are independent of the direction of travel and, therefore, cannot derive from the gradient of a function.
In broad terms, a reciprocating machine consists of a device that includes a moveable member, such as a piston, subject to a variety of configurational forces. Most reciprocating machines are designed to perform a particular function and their functionality is the main focus of machine design. When efficiency is of concern, the design is normally optimized by reducing frictional forces and heat losses while retaining the desired functionality of the machine.
Reciprocating heat engines are characterized by forces arising from the compression or decompression of the working medium in response to a displacement of the reciprocating member, i.e., the piston. The working medium may take the form of a gas, such as air or a fuel-air mixture, a liquid, a solid, or any combination thereof. If the reciprocating motion is periodic in nature, that is predictable as to the location of the reciprocating member as a function of time, then the forces are equally so and the result is a force that can be determined solely by the location of the reciprocating member. This meets the requirement of being a conservative force. The effect of these conservative forces on the efficiency of a heat engine has been traditionally, and pointedly, ignored in conventional engine-performance analysis and design on the seemingly realistic assumption that the cyclical nature of the process eliminates any net effect. This invention is based on the discovery that this assumption is in error.
The efficiency of reciprocating heat engines is analyzed conventionally using the applicable laws of thermodynamics. Referring to FIG. 1, wherein a generic reciprocating machine, HE, converting heat Q into work W is illustrated schematically, the first law of thermodynamics requires thatQ=W+dE,  (1)where E is the internal energy of the system (from F. Reif, Fundamentals of Statistical and Thermal Physics, McGraw-Hill, New York, 1965, pp. 186-187). Equation 1 defines a differential energy-balance requirement governing all thermodynamic processes. Since, by definition, each cycle begins and ends in the same thermodynamic state, the internal energy of the system (a state function) must be the same at the completion of each cycle (that is, ΔE=0 for the cycle). This leads to the theorem of Poincaré regarding cyclical processes,ΔQ=ΔWΔQ≡Qin−Qout  (2)ΔW=Wout−Win(See Kalyan Annamalai and Ishwar K. Puri, Advanced Thermodynamics Engineering, CRC Press, Boca Raton (2002) p. 65).
The efficiency of such a cyclical process is defined as the ratio of the net useful energy change produced to the energy input required to produce that change. For engines, the input consists of heat, Qin, and the output is the net work, ΔW, performed by the engine. Therefore, engine efficiency is given by
                    ∈                  =                                                    Δ                ⁢                                                                  ⁢                W                                            Q                in                                      =                                                            Δ                  ⁢                                                                          ⁢                  Q                                                  Q                  in                                            =                                                                                          Q                      in                                        -                                          Q                      out                                                                            Q                    in                                                  =                                  1                  -                                                                                    Q                        out                                                                    Q                        in                                                              .                                                                                                          (        3        )            
The cyclical operation of heat engines has been traditionally analyzed using pressure-volume (PV) diagrams, as illustrated in FIG. 2. Heat engines operate clockwise around the diagram while refrigerators and compressors proceed counter-clockwise. With reference to engines, segment I of the cycle depicted in the figure, which is a realistic hybrid of the ideal Otto and Diesel cycles described in the literature, corresponds to the adiabatic compression of the working medium in the engine. Segment II is an increase in pressure caused by the heating of the working medium under constant volume conditions. In internal combustion engines, segment II is associated with the Otto-cycle, spark-ignition of the fuel-air mixture that comprises the working medium. Segment III represents heating of the working medium where expansion and heat addition are balanced to maintain constant pressure. This is associated with the injection-controlled fuel burning phase of Diesel-cycle internal combustion engines. Segment IV corresponds to the adiabatic expansion of the working medium caused by the very high pressure produced by the heating of the working medium. Finally, segment V is the constant-volume reduction in the pressure and temperature of the working medium to return it to its initial state. This segment is identified with the process of exhausting spent fuel and replacing it with a fresh fuel-air mixture in internal combustion engines.
Based on the PV diagram of FIG. 2, those skilled in the art will readily recognize that work is performed during segments I, III and IV of the cycle, while heat/material is transferred in segments II, III and V. According to the integral definition of work,
                                          W            in                    =                                    W              I                        =                                          ∫                                  V                  1                                                  V                  2                                            ⁢                              p                ⁢                                                                  ⁢                                  ⅆ                  V                                                                    ,                            (        4        )                                                      W            out                    =                                                    W                III                            +                              W                IV                                      =                                                            ∫                                      V                    3                                                        V                    4                                                  ⁢                                  p                  ⁢                                                                          ⁢                                      ⅆ                    V                                                              +                                                ∫                                      V                    4                                                        V                    5                                                  ⁢                                  p                  ⁢                                                                          ⁢                                      ⅆ                    V                                                                                      ,        and                            (        5        )                                                      Δ            ⁢                                                  ⁢            W                    =                                                    W                out                            -                              W                in                                      =                                                            W                  III                                +                                  W                  IV                                -                                  W                  I                                            =                              ∮                                  p                  ⁢                                      ⅆ                    V                                                                                      ,                            (        6        )            where the work subscript corresponds to the area under the matching section of the curve.
It is also understood in the art, as specified in Equation 6, that the area enclosed by the diagram measures the net work done in a cycle. This has been historically interpreted as being consistent with the notion that conservative forces have no net effect on the efficiency of the system. That is, since the work associated with the area under the segment labeled I is common with the work associated with segments III and IV, but opposite in sign, its contribution to the total work done in a cycle is reduced to zero. Therefore, it has been considered not to have any effect on the efficiency of the system.
The Otto-cycle engine, typically implemented as today's spark-ignition gasoline engine, is analyzed, under an ideal implementation, as if points 3 and 4 of the curve of FIG. 2 were coincident. Similarly, the ideal Diesel cycle is assumed to have coincident points 2 and 3. Both ideal cases are only theoretical in nature, with actual operation of either engine tending more toward the mixed case shown in the figure.
The compression ratio of a reciprocating piston engine is defined as
                                          r            c                    =                                    V              1                                      V              2                                      ,                            (        7        )            where V1 and V2 are the maximum and minimum volumes, respectively, assumed by the working medium during a cycle of operation. Assuming a ratio, γ, of constant-pressure to constant-volume specific heats of the working medium (γ=cp/cV), it can be shown that the maximum attainable efficiency of such an engine is given byεtrad=1−rc1-γ.  (8)
Based on Equation 8, engine designers have stressed for decades the goal of maximizing the compression ratio of the engine in order to achieve the greatest engine efficiency. Unfortunately, increasing the compression ratio is not without difficulty in an internal combustion engine because fuel tends to spontaneously ignite at relatively low values of compression. Thus, the initial work to maximize the efficiency of the Otto-cycle engines emphasized the development of fuel additives that served to increase the compression ratio at which this spontaneous combustion occurred. Alternatively, Diesel-cycle engines maximize the compression ratio by injecting fuel after maximum compression is reached, which in turn produces spontaneous combustion of the fuel. By injecting droplets of fuel, as opposed to a gaseous fuel/air mixture, the fuel burns fairly slowly, thereby producing a roughly constant-pressure burning characteristic corresponding to the conditions of segment III in FIG. 2.
Such efforts at maximizing compression ratios to optimize the efficiency of internal combustion engines were essentially exhausted by the time of the oil crisis in the 1970s. Therefore, engineers turned to the next most well-known impediment to engine efficiency; that is, the incomplete burning of the fuel introduced into the engine. To that end, engines were equipped with fuel-injection systems that could be computer-controlled to optimize the quantity of fuel used based on data obtained from exhaust sensors in order to minimize the unburned or partially-burned fuel fraction. The results obtained from these technologies were further augmented by high-energy ignition systems and combustion-chamber structures that promoted complete burning of the injected fuel.
FIG. 3 shows efficiency data (the square data points 14 are from R. V. Kerley and K. W. Thurston, The Indicated Performance of Otto-Cycle Engines, SAE Technical Papers #620508, 1962; the round data points 16 are from D. F. Caris and E. E. Nelson, A New Look at High Compression Engines, SAE Technical Papers #590015, 1959.) and the predictive curves of the theoretical air-cycle and fuel/air-cycle models all as a function of compression ratio. The air-cycle curve 10 is simply a plot of Equation 8 using a value of 1.34 for the ratio-of specific heats as extracted from Caris, et al. for a compression ratio of 19.5:1 while the fuel/air-cycle curve 12 is obtained using varying ratios of specific heats that depend on the pre- and post-ignition constituents of the working medium, the heat of combustion of the fuel-air mixture, and an iterative estimation of the residual fuel, or mass fraction, for a cycle consistent with the conditions of the experiments. As is immediately evident from FIG. 3, the theoretical estimates provide only a qualitative relationship with the data.
There has been little recent debate in the art over the discrepancy between the theoretical curves of FIG. 3 and the experimental results. The consensus view has been that it is primarily due to unintentional heat losses through the cylinder walls of the engine. Accordingly, efforts to mitigate these losses have been made using ceramic materials with low thermal conductivity to insulate the cylinder walls. Another discrepancy between the theoretical curves and the experimental data was noted by Caris, et al. [Caris, et al. (1959)]. It lies in an apparent 17:1 compression-ratio efficiency peak that is found in the experimental data but is not predicted by the theoretical curves. The theory behind both curves 10, 12 predicts that efficiency will continue to increase with the compression ratio—not that it will peak and then decline, as shown by the experimental data.
In view of the foregoing, the accepted notion in the art has been that all parameters affecting the thermodynamic efficiency of combustion engines are well understood and that further improvements can only be achieved through incremental enhancements to the existing structures and materials already in use, rather than a better theoretical understanding of the fundamental processes involved. Therefore, any approach that might produce an improvement in the efficiency of reciprocating heat engines based on novel theoretical considerations would constitute a breakthrough in the art.